Let I be a bounded interval in R endowed with the Lebesgue measure m and let T:I→I be a measurable map with m∘T^{-1}−1≪m. The authors investigate the following question: For which T is the composition operator C_T:f↦f(T(⋅)) a well-defined (bounded) operator from W1,p(I) into itself? Some partial necessary and sufficient conditions are proved. For example, if CT maps W1,p(I), 10, then necessarily T∈W1,∞(I).
Composition operators on summable functions spaces / Marino, G.; De Cicco, V.. - In: LE MATEMATICHE. - ISSN 0373-3505. - 1:(1989), pp. 3-20.
Composition operators on summable functions spaces
De Cicco V.
1989
Abstract
Let I be a bounded interval in R endowed with the Lebesgue measure m and let T:I→I be a measurable map with m∘T^{-1}−1≪m. The authors investigate the following question: For which T is the composition operator C_T:f↦f(T(⋅)) a well-defined (bounded) operator from W1,p(I) into itself? Some partial necessary and sufficient conditions are proved. For example, if CT maps W1,p(I), 10, then necessarily T∈W1,∞(I).File allegati a questo prodotto
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